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Finding the Third Proportional to 4,214 and 7,011

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Solution

The third proportional to 4,214 and 7,011 is: 11,664.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,214 : 7,011 = 7,011 : x
  2. Step 2: Convert to fraction form
    4,214/7,011 = 7,011/x
  3. Step 3: Cross multiply
    4,214x = 7,011 × 7,011
  4. Step 4: Simplify right side
    4,214x = 49,154,121
  5. Step 5: Solve for x
    x = 49,154,121/4,214
  6. Step 6: Final answer
    x = 11,664.48

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.